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Results tagged with linear-algebra
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user 37555
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
3
votes
Accepted
An algebraic equation question
This is not possible. Suppose e.g. that $e^\beta=2$. Then we have $p+1=2(m+1)$, i.e. $\frac{p}{m}=2+\frac{1}{m}$. Hence $\frac{p}{m}$ can attain any real number $>2$, depending on what $m$ is. In gene …
6
votes
1
answer
191
views
Monte-Carlo computation of the Smith normal form
Quite some time ago I saw an article where a Monte-Carlo algorithm for computing the Smith normal form of an integer matrix was described. In this article the following problem was posed:
Suppose $P, …
1
vote
Accepted
Probabilistic statement on matrix ranks
Consider the set of $n\times n$-matrices with entries in $\{0,1\}$ which have at most $r$ distinct rows. The number of such matrices is $2^{rn}r^n$. As long as $n$ and $n-r$ tend to infinity, we have …
3
votes
Does there exist another form of the derivative for polynomials?
As there are several possibilities for $F$, here is an attempt at determining $H$.
Using the linearity of $F$ we have $H(\lambda x, y, \lambda u, v)=\lambda H(x, y, u, v)$. Taking the derivative with …